We just picked up our 2012 Model S on Friday from our nearest service center, as it needed an MCU replacement (probably the eMMC issue) and wouldn't charge. Everything worked out as well as could be expected for an out-of-warranty car. The folks at the service center tried hard to make us happy and went the extra mile.
My only frustration was not being able to contact the service center directly, before dropping the car off. Last Monday, the car's battery charge was down to about 40 miles and dropping daily in the cold, and the soonest appointment at the only service center safely within battery range was two weeks out. After some back and forth and a total of at least an hour on hold, I asked the folks on Tesla's national support line if I could just drop off the car without an appointment before the battery dropped further; I didn't want to risk having to get the car towed. The service center then called and gave me a same-day appointment. They clarified that, in situations like this, it's perfectly fine to simply bring in the car without an appointment.
I'm very pleased that the service center was able to get a replacement MCU into our car within four days. I was told that they had to obtain the MCU from another service center in our region. They were very proactive at communicating via texts and phone calls to update me on the car's status every day. Unfortunately, that channel of communication goes away once the job is "closed out". Thankfully, the car is working well again, so this isn't a concern for us at this time.
There definitely seems to be some frustration among service employees that customers can't simply call local service centers. The app is great, but sometimes you just need to talk to someone to figure out what to do. Our local service center, which just opened weeks ago, really seems to want to give customers a positive experience in spite of a corporate-level communication policy that needs to be revamped. They clearly have employees who believe in Tesla's mission, who also happen to drive Tesla vehicles or other EVs.